NCU Qyburn's ability to spend an order token when your opponent takes Swords says "Attacker counts as having -1 rank for attack dice". There is no spot on a combat unit's card for zero ranks if they're a solo or a unit that has been knocked down to 1 rank via casualties.
Personally I would play this card as it can’t reduce an attack below 1 rank (0 attack dice) since that would be OP. Just my opinion, I didn’t find anything in the rules on this topic. If I’m wrong and CMON intended to allow 0 attack dice, it would be brutal against monster/cavalry lists.
Maybe, but monster/cavalry lists are some of the most powerful out there due to their extreme mobility. One 5 point NCU that requires your opponent to take Swords and specifically target a solo or unit with one rank left doesn't exactly seem overpowered. The other player can also play around this effect by targeting a unit other than a solo/1 rank unit because you do it before resolving the effect. This allows the Swords-taking player to re-point which unit they want for the attack.
I suppose, unless all you have left are 1 rank units which means they blocked your NCU activation for that round. I.e if I ran an all giants list I could never take swords for example.
But that is not inherently imbalanced or even powerful in the first place. You can again play around it by not taking Swords, or by taking Swords just to stop your opponent from getting it. I've taken Bags without a need to heal or a replacement effect. All I wanted was to stop my opponent from getting that heal.
So this question came up again at my LGS and we were able to get an official response from the game designer:
There is no such thing as a non-destroyed unit with zero ranks.
The lowest attack die value for a unit is red.
In the case of solos. They have only the one value (in green).
Looks like my original hypothesis was correct!
Regardless of if you believe his source or not:
Rules as Written, there is no mention of losing all your attack dice for having "zero ranks" nor any mention of zero ranks at all. However, in multiple places there IS the wording of "LOWEST" attack die value. (A superlative, lowest, indicating you can't go any lower) since that is the lowest attack die value possible, using the rules as written, you cannot be reduced below that value. It would simply be a waste of your NCU to apply a rank penalty for attacks to a unit that is already only at one rank. Make a different play or suffer the consequences of your choice.